Optimised uncertainty and cost operating characteristics: new tools for conformity assessment. Application to geometrical product control in automobile industry

SP Technical Research Institute of Sweden, Measurement Technology, Box 857, SE-501 15 Borås, Sweden

^⋆ Correspondence: leslie.pendrill@sp.se

Received: 5 August 2010
Accepted: 20 August 2010

Abstract

Translating measurement uncertainty into terms of effective impact associated with manufacture, testing and incorrect assessment gives a more “stakeholder” motivated (and ultimately optimised) approach to decision-making in conformance assessment. Recently developed decision-theory tools include the “optimized uncertainty” methodology and the “operating cost characteristic”. Overall costs, E, consisting of a sum of testing costs, D, and the costs, C, associated with customer risk, can be calculated with the expression: $\mathit{E}\mathrm{\left(}\mathit{\eta ,\sigma }\mathrm{\right)}\mathrm{=}\mathit{D}\mathrm{\left(}\mathit{\eta ,\sigma }\mathrm{\right)}\mathrm{+}\mathit{C}\mathrm{\left(}\mathit{\eta }\mathrm{\right)}\mathrm{=}\frac{\mathit{D}}{{\mathit{\sigma }}^{\mathrm{2}}}\mathrm{+}{{}^{\mathrm{\int }}}_{\mathit{\eta }\notin {\mathit{R}}_{\mathit{PV}}}\mathit{C}\mathrm{\left(}\mathit{\eta }\mathrm{\right)}\mathrm{·}\mathit{g}\mathrm{\left(}\mathit{\eta }|\mathit{\eta ̂}\mathrm{\right)}\mathrm{·}\mathit{d\eta }$ with $\mathit{\eta ̂}\mathrm{\in }{\mathit{R}}_{\mathit{PV}}$, where R_PV denotes the region of permissible values and σ is a measure of dispersion. A complete, 3D surface of overall cost can indicate the optimum level of measurement effort of these two ranges, as recently published by the author in a wide range of applications: optimized acceptance sampling; optimized testing of measurement instruments; and an analysis of optimised calibration intervals and “guard-banding”. This approach is illustrated in the present work for the example of geometrical product control in the car industry, specifically the gap in vehicle closure panels taking account of customer dissatisfaction.